An Algorithm to Automatically Generate the Combinatorial Orbit Counting Equations

PloS One
Ine MelckenbeeckMario Pickavet

Abstract

Graphlets are small subgraphs, usually containing up to five vertices, that can be found in a larger graph. Identification of the graphlets that a vertex in an explored graph touches can provide useful information about the local structure of the graph around that vertex. Actually finding all graphlets in a large graph can be time-consuming, however. As the graphlets grow in size, more different graphlets emerge and the time needed to find each graphlet also scales up. If it is not needed to find each instance of each graphlet, but knowing the number of graphlets touching each node of the graph suffices, the problem is less hard. Previous research shows a way to simplify counting the graphlets: instead of looking for the graphlets needed, smaller graphlets are searched, as well as the number of common neighbors of vertices. Solving a system of equations then gives the number of times a vertex is part of each graphlet of the desired size. However, until now, equations only exist to count graphlets with 4 or 5 nodes. In this paper, two new techniques are presented. The first allows to generate the equations needed in an automatic way. This eliminates the tedious work needed to do so manually each time an extra node is added to th...Continue Reading

References

Jul 31, 2004·Bioinformatics·N PrzuljI Jurisica
Jan 24, 2007·Bioinformatics·Natasa Przulj
Dec 18, 2013·Bioinformatics·Tomaž Hočevar, Janez Demšar

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Citations

Feb 10, 2017·PloS One·Tomaž Hočevar, Janez Demšar
Jan 17, 2019·BMC Bioinformatics·Ine MelckenbeeckMario Pickavet
Apr 6, 2017··Ali PinarVaidyanathan Vishal

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Software Mentioned

ORCA
ISMAGS

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